Fatty Acid Content in Biomasses: State-Of-The-Art and Novel Physical Property Estimation Methods

Hindawi International Journal of Chemical Engineering Volume 2019, Article ID 2430234, 25 pages https://doi.org/10.1155/2019/2430234

Research Article Fatty Acid Content in Biomasses: State-of-the-Art and Novel Physical Property Estimation Methods

Ana M. Sousa ,1 Thalles A. Andrade ,2 Massimiliano Errico ,2 Jose´ P. Coelho ,3,4 Rui M. Filipe ,1,3 and Henrique A. Matos 1

1CERENA/DEQ, Instituto Superior Tećnico, Universidade de Lisboa, Av. Rovisco Pais 1, Lisboa, Portugal 2Department of Chemical Engineering, Biotechnology and Environmental Technology, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark 3Instituto Superior de Engenharia de Lisboa, Instituto Politećnico de Lisboa, 1959-007 Lisboa, Portugal 4CQE, Instituto Superior Tećnico, Universidade de Lisboa, Av. Rovisco Pais 1, Lisboa, Portugal

Correspondence should be addressed to Massimiliano Errico; [email protected]

Received 14 June 2019; Accepted 22 September 2019; Published 23 November 2019

Academic Editor: Maurizio Volpe

Copyright © 2019 Ana M. Sousa et al. (is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In line with the growing environmental awareness developed along the last decades, modern societies are urged to evolve into sustainable economics where the reuse of organic wastes represents the key feedstock for a green transaction. (e oil phase obtained from different biomasses has the potential to be a source of food supplements, medicines, cosmetics, or feedstock for biofuel production. In the present work, the composition of 104 different biomasses including seeds, peels, flowers, plants, and leaves has been reviewed for the lipid content. Based on the most frequent fatty acids screened, experimental data for normal boiling point temperature, normal melting point, critical properties, and acentric factor were collected and compared with the most common estimation methods, which are functions of the molecular structure and interaction between different functional groups. New predictive equations have been proposed to reduce the estimation deviation and to provide simple correlations to be used in simulation software when dealing with biomass processes. For all the properties, the estimations proposed have an absolute average deviation equal to or lower than 4.6%.

1. Introduction with the chemical industry and petroleum exploration [2], incorporated in the broader research initiative aiming to (e development of sustainable processes can be pursued develop integrated processes and product design for sus- through multiple paths, among which decreasing wastes, tainable biorefineries [3]. increasing efficiency in industrial processes, mitigating en- Fatty acids are long hydrocarbon chains with a terminal vironmental and human risks, reducing pollutant agents, carboxyl group. (ey can be obtained from rather abundant and fostering energy production from renewable sources organic compounds, including organic matter wastes [4, 5] play unquestionable roles. or nonedible oils [6, 7]. Fatty acids are characterized by an Within this context, biomass appears as a valuable outstanding range of applications within the energy domain, feedstock to recover several compounds and/or produce such as biofuels [8], and flow improvers for crude oils [9–12], energy to answer the global consumption growth without or within other high end industries such as food supple- creating a negative legacy to the next generations [1]. In fact, ments [13], cosmetics [14], medicines, and drugs [15, 16]. the widespread employment of biomass not only bears the Fatty acids, often referred to as fats, are used in the potential of recovering industrial wastes as a valuable resource human body to store excess energy, and they constitute the but also leverages the energy and industrial productions building blocks for membrane cells [17, 18]. Moreover, as through efficient and less polluting engineering processes. recommended by the Food and Agriculture Organization of (is work is deemed to study the potential of fatty acids the United Nations [19], there is convincing evidence that in addressing significant multidisciplinary issues associated some fatty acids like the linoleic acid and the alpha-linoleic 2 International Journal of Chemical Engineering acid are indispensable for human health even if they cannot centrally, for the production of valuable final products or be synthesized. intermediates with applications in pharmaceutical, food and Considering the broad range of fatty acid applications, beverages, or even nutraceutical fields [21]. Subsequently, an extensive review of their amount and composition in waste biomass effluents could be treated to produce lower different biomasses has been drawn. added-value products, e.g., insecticides or pesticides, or used Such remarkable potential opens the definition of new as feedstock for biofuel production. industrial processes for fatty acid recovery from different A total of 104 different types of oils obtained by ex- biomasses contributing to valorize poor feedstocks and to traction of different biomasses were collected from the reduce their environmental impact when treated as wastes. scientific literature to identify the most common and Such approach paved the way in applying strategies deemed frequent fatty acids. (e list of oil sources and main fatty to foster sustainability on an industrial scale. acid composition is reviewed in Table 1. (e information Within a biorefinery approach, the target compounds are was collected and summarized from different published recovered or obtained from the biomass through a series of works, and when available, the minimum and maximum processes classified as thermochemical, biochemical, me- concentration values were reported. In some cases, the chanical/physical, and chemical [20]. It means that, in order to percentage of oil content in the biomass matrix was also move from the definition of the biomass potential in re- included. (is value could be useful to determine a possible covering or obtaining some compounds to the process setup, a upper bound oil extraction yield from the biomass matrix. reliable model must be available to design the single unit In Table 1, 16 fatty acids were listed since, according to the operation and to define the process global performance and sources reviewed, they appear in the oil in a significant profitability. Product and process design rely on the knowledge amount. of the properties of chemical compounds and their mixtures. Ricinoleic acid, lesquerolic acid, and elaeostearate acid, Although large databases of experimental data are available, the main constituents of castor oil, lesquerella oil, and tung covering the complete set of compounds, mixtures, and op- oil, respectively, were not reported since they do not appear erating conditions is a huge task that may not be economically in the other biomasses listed. Information about their feasible. Property estimation models for physical properties are quantity is provided in Table 1 notes. widely used when experimental data are not available. Figure 1 shows the average of each fatty acid yield in the Unlike what can be found in published research con- biomasses and their frequency of appearance. cerning thermophysical properties of pure compounds, this (e fatty acid yield average was obtained by considering work has been focused on the most important temperature- the values reported in Table 1. For those cases where a yield independent physical properties of the main fatty acids interval is indicated, the average was calculated. (e fre- found in biomass feedstocks. (ese properties are also es- quency of appearance expresses the occurrence of fatty acid sential in improving the processes modeling, in the for- in the set of biomasses. mulation of product portfolios and for the composition Regarding the saturated fatty acids, palmitic acid (C16 : 0) assessment of the generated pollutants. and stearic acid (C18 : 0) are the ones with the highest content Published prediction methods were critically analyzed and frequency in all the bio-oils examined. Considering given the scarcity of experimental data for determining the the unsaturated fatty acids, oleic acid (C18 :1), linoleic acid relevant physical properties. Considering current methods (C18 : 2), and linolenic acid (C18 : 3) are the most plentiful shortcomings for the intended applications and using the compounds identified in the reported bio-oils. However, National Institute of Standards and Technology (NIST) since the average yield reported in Figure 1 was evaluated database as a reference, innovative estimation methods were considering the distribution of the single fatty acids, a more developed. Such correlation’s novelty is not only limited to a revealing indicator is the average minimum and average higher accuracy but also finds a significant advantage in its maximum, reported in Figure 2 as a grey rectangle. (e simplicity, given the use of molecular weight (MW) and the minimum and maximum averages were published together maximum number of double bonds (DBs) in the molecule as with the absolute minimum and absolute maximum. On the input. To sum up, a reliable method for the estimation of one hand, taking caprylic acid as an example, its average yield fatty acid (FA) physical properties was developed. (erefore, range is from 0.2% to 5.2%, which is a very narrow range, a set of six new correlations have been proposed to reduce while the absolute maximum is 11.4%. On the other hand, the estimation deviation of boiling point, melting point, when palmitoleic acid, oleic acid, and linoleic acid are con- critical properties, and acentric factor. sidered, their amount can extensively vary. Such a tool will be of paramount importance in proposing strategies that congregate high-value addition in industrial 3. Fatty Acid Classification processes with the use of abundant biomass and the reuse of potentially polluting waste from food or other related pro- Oil extracts from biomasses comprise saturated and un- cesses, such as the waste from olive oil or wine manufacture. saturated fatty acids with long carbon chain, which can be employed in integrated processes for sustainable bio- 2. Review on Fatty Acid Content in Biomasses refineries. To highlight the differences between the molecules, the different fatty acids were identified based on the A biorefining process is based on the usage of selected number of carbon atoms (CN) and the number of carbon- biomass(es) treated in a smaller or larger unit, locally or carbon double bonds (DB). Table 1: Fatty acid content in the selected biomasses expressed in weight. Engineering Chemical of Journal International

Palmitic Palmitoleic Stearic Linoleic α-Linolenic Arachidic Eicosenoic Eicosadienoic Lignoceric Oil Caprylic Oleic acid, Capric acid, Lauric acid, Myristic acid, acid, acid, acid, acid, acid, acid, acid, acid, Behenic acid, Erucic acid, acid, Others Biomass content acid, C18 :1 References C10 : 0 (%) C12 : 0 (%) C14 : 0 (%) C16 : 0 C16 :1 C18 : 0 C18 : 2 C18 : 3 C20 : 0 C20 :1 C20 : 2 C22 : 0 (%) C22 :1 (%) C24 : 0 (%) (%) C8 : 0 (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) Alexandrian laurel (Calophyllum NA 13.9 0.2 15.1 40.3 25.6 0.2 0.3 [22] inophyllum) Almond NA 5.07–6.78 0–0.5 0–1.4 57.54–73.94 19.32–35.18 0.04–0.10 0–0.9 [23, 24] Andiroba (Carapa guianensis) NA 27 1 7 49 16 [25] Argemone mexicana 30–40 0–0.1 14.1–15.3 0–1.3 3.7–9.8 34.3–45.8 29.0–44.2 0–0.3 0–0.3 0–0.2 [26] Avocado seeds 1.1–1.6 0–0.28 0.20–0.60 0.54–1.30 17.7–20.85 1.79–4.60 0.90–1.50 17.41–24.1 35.30–38.89 4.10–6.58 0.04–0.80 0.45–2.00 0.40–1.11 0–0.12 1.68–3.30 [27, 28] Babassu kernel (Orbignya sp.) 60–70 0–5 0–6 35–48 13–16 9–10 2–4 14–17 2–5 0–5 [25, 29, 30] Bay laurel fruit NA 18.3 3.5 21.8 0.5 3.8 30.9 20.5 0.4 0.3 [31] Bay laurel leaves NA 26.2 4.5 25.5 0.3 3.1 10.6 11.3 17.1 1.4 [24, 31] Bitter almond NA 0.1 10.3 3.9 33.9 46.0 4.8 0.2 [32] Black currant (Ribes nigrum L.) 2.2 6.4 1.6 16.1 57.8 13.2 0.2 4.7 [33] Burdock seeds 15–20 7 20 69 4 [34] Camelina 38–47 0.05–0.2 5.1–6.8 0–0.3 2.7–3.4 14.3–19.7 14.3–19.6 28.6–38.4 0.25–1.83 11.9–16.8 1.3–2.2 0.2–1.4 2.3–4.2 0–0.14 0–0.8 [35–38] Carapa seeds 51 0.5 25.3 10.5 57.8 5.9 [39, 40] Carob seeds 1.73–1.84 10.3–12.0 0.6 3.5–4.6 28.1–31.8 49.1–51.0 1.4–1.7 0.6 1.7–2.5 [41] Castor oil 42–54 0.84–1.30 0.78–3.60 2.92–4.90 1.27–5.40 0–0.78 0–0.66 0–0.63 84.7–89.6a [42–47] Chia (Salvia hispanica L.) 25–38 5.5–8.9 2.7–4.8 5.3–8.4 15.7–26 50.0–69.3 [48–50] Chokeberry (Aronia melanocarpa L.) 1.93 5.1 1.1 21.4 71.1 0.5 0.8 [33] Chlorophyceae (Botryococcus sp.) 6.19 20.56 8.20 4.56 44.74 6.36 15.55 [51] Chlorophyceae (Chlorella sp.) 14.05 1.60 0.86 35.72 0.85 8.53 21.50 15.30 0.36 15.27 [51] Chlorophyceae (Chlorococcum sp.) 8.21 0.86 21.65 0.90 0.50 20.60 21.30 2.81 0.42 16.53 12.66 [51] Chlorophyceae (Dunaliella salina) 6.25 36.40 5.30 50.81 7.46 [51] Coconut (copra) NA 8.0–8.9 6.0–6.2 47.0–48.8 17.0–19.9 7.8–9.7 0.1 3.0 4.4–7.0 0.8–2.2 [24, 42, 52] Corn NA 11.67–11.80 1.85–2.00 24.80–25.16 60.60–61.30 0–0.48 0–0.24 0.3 [24, 42, 43] Cottonseed NA 0.67–3.45 8.83–28.70 0.42–4.05 0.89–14.72 10.3–30.7 20.6–62 [42, 43, 53–55] Crambe 35 2.07 0.70 18.86 9.00 6.85 2.09 0.80 58.51 1.12 [43, 56, 57] abyssinica Crataegus NA 0.26 0.20 13.21 2.23 33.78 44.60 1.37 1.01 [58] monogyna Cumaru (Dipteryx odorata) NA 23 7 37 29 4 [25] Cuphea viscosissima NA 0.3 64.7 3.0 4.5 7.0 0.9 12.2 6.7 [59] Cyanophyceae (Calothrix sp.) 3.42 26.95 6.55 3.99 55.52 6.94 [51] Cyanophyceae (Leptolyngbya sp.) 3.23 13.74 1.53 4.73 69.52 5.36 1.56 3.57 [51] Cyanophyceae (Lyngbya sp.) 2.52 1.23 26.49 5.37 3.24 54.53 4.00 5.15 [51] Cyanophyceae (Nostoc muscorum) 3.22 26.89 54.01 7.85 11.24 [51] Cyanophyceae (Oscillatoria acuta) 4.47 13.61 8.53 68.68 9.17 [51] Cyanophyceae (Oscillatoria marina) 6.61 0.21 18.74 2.01 4.74 63.15 8.90 0.65 1.60 [51] Cyanophyceae (Spirulina platensis) 7.75 22.53 2.34 5.21 53.54 7.74 5.52 [51] Cyanophyceae (Synechococcus sp.) 4.2 8.74 82.12 1.73 5.45 1.94 [51] Ethiopian mustard (Brassica carinata) NA 2.9–3.1 1.0 9.7–33.9 8.2–16.8 1.1–16.6 0.7 10.9 42–42.5 9.6 [60–62] Euphorbia lathyris L. 46 5.53–6.80 0–0.50 0–1.98 78.20–81.46 3.71–4.62 2.78–7.85 0–0.50 0–0.20 [63, 64] Forsythia suspensa 30 5.65 1.99 18.68 72.89 0.79 [65] Goji berry (Lycium barbarum L.) NA 15.1–21.8 1.0–3.1 2.61–4.78 16.7–22.4 37.0–44.0 1.0–3.0 0.48–6.78 [66] Grape seeds NA 0–0.09 7.2–10.35 3.8–6.67 12.80–29.1 52.26–65.33 0–0.6 0–0.38 0–0.10 [58, 67] Hazelnut kernel (Corylus avellana) 51–75 4.9–5.1 0.2–0.4 2.1–2.6 76.9–83.6 8.5–13.1 0.2 0–0.2 0–0.3 0–0.4 [24, 42, 68] Jatropha curcas 50–60 0–0.31 13.23–14.9 0.85–0.88 5.40–9.5 40.5–45.79 32.27–36.99 0–0.3 0–1.93 [60, 64, 69, 70] Jojoba (Simmondsia Chinensis) 45–55 0.30–3.50 3.10–9.00 0.60–2.20 28.20–46.30 0.20–3.10 0.30–3.80 20.80–51.50 0–14.5 1.40–4.40 0.50–19.70 [71–73] Karanja (Pongamia pinnata) 30–40 7.4–11.6 3.8–7.5 51.6–65.6 15.4–16.6 0–4.4 3.4–12.7 [60, 70, 74] Kusum (Schleichera trijuga) NA 0.31 15.54 10.35 11.11 27.08 6.14 15.79 6.17 0.08 0.01 7.42 [75] Lemon seeds 33.4–41.9 23.5–29.4 0.4–0.9 4.1–6.5 24.8–29.3 33.2–36.3 3.2–7.8 0.5–1.5 [76] Lesquerella fendleri 0.3 1.0 0.4 1.8 13.6 6.7 10.2 0.8 0.9 64.3b [47] Linseed 35–45 4.92–5.1 0.3 2.41–2.5 18.9–19.7 18.03–18.1 54.94–55.1 [42, 43, 60] Mahua (Madhuca indica) 35–40 0–0.14 16.0–28.2 18.97–25.8 37.2–51.0 8.9–19.5 0–0.16 [60, 70, 77] Meliaceae (Aphanamixis polystachya) NA 18.4 0.3 11.8 18.3 26.7 23.2 0.5 0.2 0.6 [78] Mesua ferrea seeds 55–57 0.05–2.13 10.85–13.64 0–0.09 13.65–14.19 50.71–55.93 13.68–19.47 0–0.32 0–1.3 0.18–2.92 0–0.35 0–0.19 [79–81] Michela champaca 45.0–45.5 0–0.57 15.8–32.52 6.9–13.39 2.5–8.88 6.03–22.3 30.72–42.5 0–0.71 [82, 83] Milk thistle NA 7.3–8.4 4.6–6.8 22.8–28.9 49.7–53.6 0–0.3 2.9–4.3 0.8–0.9 2.3–2.9 0.6–0.8 [84] Milkweed seed (Calotropis gigantea) NA 15.5–16.7 0–0.3 9.0–10.50 30.3–47.2 27.1–36.3 0–0.8 0–0.6 0–0.1 0–0.4 [85] Moringa seed 38–40 0–0.1 6.5–13.8 1.1–2.0 4.7–6.0 72.1–72.2 1.0–2.5 0–0.9 3.8–4.0 0.9–2.0 [86, 87] Mustard seed NA 0.05 5.54 0.21 1.51 8.83 10.79 20.98 1.21 5.27 0.70 1.09 37.71 1.68 4.43 [36] Neem 20–30 0–0.26 13.6–18.1 0–0.2 14.2–24.1 44.5–61.9 2.3–18.3 0.2–3 0.8–3.4 [60, 88–91] Niger (Guizotia abyssinica) 30 9.2 10.1 9.0 71.7 [92] Olive kernel NA 5.0 0.3 1.6 74.7 17.6 0.8 [24, 42] Olive pomace 8.5–14.9 0–0.04 9.37–16.20 0.68–0.80 2.68–3.00 69.3–79.0 7.20–12.70 0.30–0.87 0–0.58 0–0.40 0–0.22 [93–95] Opium poppy (Papaver somniferum L.) NA 9.79 0.13 1.93 11.94 74.47 1.7 [96] Orange peel NA 38.6 4.1 57.2 0.1 [97] Palm (Elaeis sp.) NA 0–0.3 0–1.1 35–43 0–0.3 4–7 40–44 10–14 0–0.2 0–0.3 0–1.1 [25, 35, 42, 98] Corozo palm/Maca´uba(Acrocomia NA 5.0 50.9 13.1 7.6 3.0 17.9 2.5 [99] aculeata) Peanut (Arachis hypogaea) 40–50 6.7–11.4 1.73–3.99 47.06–78.2 4.4–32.0 0.19–0.93 0–3.0 0–1.9 2.52–3.93 0–0.73 1.23–1.83 0–0.1 [42, 43, 68, 100, 101] Peppers (Capsicum) NA 10.6–14.4 2.7–3.9 5.4–7.6 73.9–77.9 [102] Pequi (Caryocar sp.) NA 40 2 47 4 7 [25] 3 4

Table 1: Continued.

Tobacco seed (Nicotiana Engineering Chemical of Journal International 38 0.09–0.17 3.0–10.96 0–0.20 3.34–5.0 12.14–16.0 67.75–72.98 0.69–4.20 0.20–0.25 0.12–0.13 0.07–0.12 0–0.04 0.69–3.12 [132–135] tabacum L.) Tung (Vernicia montana) NA 2.3 2.4 5.6 6.3 0.1 0.2 0.9 0.1 82.2c [136–140] Walnut (Juglans regia) 52–70 7.2 0–0.2 1.9–2.6 15.1–18.5 56.0–60.7 12.8–16.2 0–0.2 0–0.5 [24, 42, 68] Wheat germ NA 0–0.13 17.4–18 0.17–0.23 0–0.7 16.1–16.5 55.1–57.7 7.9 0–0.28 [141, 142] Wheat grain NA 11.4 0.4 20.6 1.0 1.1 16.6 56.0 2.9 1.8 [24] Waste coﬀee ground 10–15 33.99 10.91 7.16 23.27 4.04 20.6 [143] Yellow oleander seed (?evetia 60–65 15.03–23.28 0–0.39 6.16–10.71 43.72–44.35 19.85–31.99 0–0.79 0.79–2.41 0–0.49 [144–146] peruviana) Zanthoxylum bungeanum 24–28 10.3 10.8 1.1 35.9 24.8 15.9 1.2 [147] aCastor oil contains 89.6 ricinoleic acid. bLesquerella oil contains 57.6 lesquerolic acid. cTung oil contains 82.2 elaeostearate acid. International Journal of Chemical Engineering 5

35 100 30 90 80 25 70 20 60 50 15 40 10 30 Frequency (%) Frequency

Average yield (%) Average 20 5 10 0 0 Oleic acid, C18:1Oleic acid, Lauric acid, C12:0Lauric acid, Erucic C22:1 acid, Capric acid, C10:0 acid, Capric Stearic acid, C18:0 acid, Stearic Caprylic C8:0 acid, Behenic C22:0 acid, Linoleic acid, C18:2Linoleic acid, Palmitic acid, C16:0 acid, Palmitic Myristic acid, C14:0 acid, Myristic Arachidic acid, C20:0 acid, Arachidic Lignoceric C24:0 acid, Eicosenoic acid, C20:1 acid, Eicosenoic Palmitoleic acid, C16:1 acid, Palmitoleic -Linolenic acid, C18:3 acid, α -Linolenic Eicosadienoic acid, C20:2 acid, Eicosadienoic

Average yield Frequency Figure 1: Percentage and frequency of each fatty oils in the biomasses reported in Table 1.

100 90 80 70 60 50 40 30 20 10

Quantity per lipid fraction (%) per lipid Quantity 0 Oleic acid, C18:1Oleic acid, Lauric acid, C12:0Lauric acid, Erucic C22:1 acid, Capric acid, C10:0 acid, Capric Stearic acid, C18:0 acid, Stearic Caprylic C8:0 acid, Behenic C22:0 acid, Linoleic acid, C18:2Linoleic acid, Palmitic acid, C16:0 acid, Palmitic Myristic acid, C14:0 acid, Myristic Arachidic acid, C20:0 acid, Arachidic Lignoceric C24:0 acid, Eicosenoic acid, C20:1 acid, Eicosenoic Palmitoleic acid, C16:1 acid, Palmitoleic -Linolenic acid, C18:3 acid, α -Linolenic Eicosadienoic acid, C20:2 acid, Eicosadienoic Figure 2: Average minimum and maximum (grey rectangle) and absolute maximum and minimum (interval lines).

While saturated acids are solid at room temperature, the from the proposed correlations were compared using dif- unsaturated are in the liquid state. Furthermore, saturated ferent deviation indexes: and unsaturated fatty acids also differ regarding their (i) (e absolute deviation (AD) is defined as structure. While saturated fatty acids have a linear molecule, the introduction of one or more double bonds promotes the AD � |estimated value − experimental value|. (1) molecule twisting and the possibility of geometrical isom- erism. Figure 3 reports the difference in the structure for the (ii) (e relative deviation (RD) and the absolute relative fatty acid with 18 carbon atoms and 0, 1, and 2 double bonds. deviation (ARD) are as follows, respectively: Following the analysis summarized in Figures 1 and 2, the most common saturated and unsaturated fatty acids estimated value − experimental value RD � × 100, (2) identified are presented in Table 2 together with the cor- experimental value responding CAS number and their molecular weight. ARD �|RD|. (3) 4. Physical Properties Temperature nondependent properties, namely, normal (iii) (e average absolute deviation (AAD) is given as boiling point, normal melting point, critical properties, and follows: acentric factor, were evaluated in this section. N 1 Using the NIST database as a reference, the values ob- AAD � � AD. (4) n tained from the different estimation models and the values i�1 6 International Journal of Chemical Engineering

(a) (b) (c) Figure 3: C18 : 0, stearic acid C18H36O2 (a); C18 :1, oleic acid C18H34O2 (b); C18 : 2, linoleic acid C18H32O2 (c).

Table 2: Fatty acids selected for the property evaluation classiﬁed by name, CAS number, and molecular weight. CN : DB Molecular formula Common names and IUPAC name CAS no. MW (g/mol)

C8 : 0 C8H16O2 Caprylic acid, n-octanoic acid 124-07-2 144.21 C10 : 0 C10H20O2 Capric acid, n-decanoic acid 334-48-5 172.27 C12 : 0 C12H24O2 Lauric acid, n-dodecanoic acid 143-07-7 200.32 C14 : 0 C14H28O2 Myristic acid, tetradecanoic acid 544-63-8 228.38 C16 : 0 C16H32O2 Palmitic acid, hexadecanoic acid 57-10-3 256.43 C18 : 0 C18H36O2 Stearic acid, n-octadecanoic acid 57-11-4 284.48 C20 : 0 C20H40O2 Arachidic acid, eicosanoic acid 506-30-9 312.54 C22 : 0 C22H44O2 Behenic acid, docosanoic acid 112-85-6 340.59 C24 : 0 C24H48O2 Lignoceric acid, tetracosanoic acid 557-59-5 368.65 Palmitoleic acid, (9Z)-hexadec-9-enoic acid, cis-9- C16 :1 C H O 373-49-9 254.41 16 30 2 hexadecenoic acid Oleic acid, (9Z)-octadec-9-enoic acid, n-octadecenoic C18 :1 C H O 112-80-1 282.47 18 34 2 acid, [omega-9 fatty acid (18 :1 ω9)] Paullinic acid, 13-eicosenoic acid, [omega-7 fatty acid 29204-02-2 (20 :1 ω7)] Gondoic acid, cis-gondoic acid, cis-11-eicosenoic acid, 11-eicosenoic acid, 11Z-eicosenoic acid, cis-11-icosenoic C20 :1 C H O 5561-99-9 310.52 20 38 2 acid, (11Z)-icos-11-enoic acid, [omega-9 fatty acid (20 :1 ω9)] Gadoleic acid, 9-eicosenoic acid, [omega-11 fatty acid 17735-94-3 (20 :1 ω11)], (E)-icos-2-enoic acid 26764-41-0 Erucic acid, (Z)-docos-13-enoic acid, cis-13-docosenoic C22 :1 C H O 112-86-7 338.58 22 42 2 acid Nervonic acid, (Z)-tetracos-15-enoic acid, [omega-9 C24 :1 C H O 506-37-6 366.62 24 46 2 fatty acid (24 :1 ω9)] Linoleic acid, (9Z,12Z)-9,12-octadecadienoic acid, C18 : 2 C H O 60-33-3 280.45 18 32 2 [omega-6 fatty acid (18 : 2 ω6)] α-Linolenic acid, cis-9,12,15-octadecatrienoic acid, 463-40-1 [omega-3 fatty acid (18 : 2 ω3)] Gamma-linolenic acid, gamolenic acid, all-cis-6,9,12- C18 : 3 C H O 506-26-3 278.44 18 30 2 octadecatrienoic acid, [omega-6 fatty acid (18 : 2 ω6)] α-Calendic acid, (8E,10E,12Z)-octadeca-8,10,12-trienoic 5204-87-5 acid, [omega-6 fatty acid (18 : 2 ω6)]

(iv) (e root mean square deviation or relative deviation compare different liquids and represents an essential input for (RMSD) is obtained using the following equation: the estimation of other properties like the critical parameters. �� N AD2 RMSD � i�1 . (5) N 4.1.1. Estimation Methods. To determine the normal boiling point, several methods are available in the lit- (v) (e average absolute relative deviation (AARD) is erature. (e most relevant ones are summarized in defined by the following equation: Table 3. 1 N Each of these methods has been applied for the set of AARD � � ARD. (6) n fatty acids identified in Table 2. i�1 (e Joback and Reid method [148] estimates the normal T boiling point considering the group incremental value ( Bi) 4.1. Normal Boiling Point. (e normal boiling point (TB) is multiplied by the number of times the group appears in the defined as the temperature in which the vapor pressure equals compound (Ni). (e estimation formula is reported in the the value of 1 atmosphere. (e normal boiling point is used to following equation: International Journal of Chemical Engineering 7

T � 198.2 + � N · T . where Ci is the group contribution of group i and n is the B i bi (7) i number of atoms in the molecule (excluding the hydrogen atoms). (e method is valid for nonelectrolyte organic (e coeﬃcients used for the estimation of the normal boiling compounds and was developed using experimental data for point are reported as Supplementary Material in Table A1. about 2850 compounds stored in the Dortmund data bank. Constantinou and Gani [149] established the two-level Table A7 of the Supplementary Material presents the co- evaluation method reported as follows: eﬃcients correspondent to this method.

⎛⎝ ⎞⎠ TB(K) � 204.359 · ln � Ni · Tb1i + W · � Mj · Tb2j . 4.1.2. Normal Boiling Point Estimation Results. (e results i j for the normal boiling point estimated using the methods (8) described are summarized in Table 4. (e values extracted from the NIST database were accessed through the Aspen (e method is based on the first- and second-order Property software, and they were used as a reference for the group contribution. In the former, each group has a single comparison with the estimated values. (e values obtained contribution independently of the type of compound in- were checked for consistency, and it was noticed that the T T volved ( B1i). (e latter ( B2j) has the function to provide normal boiling point for the C24 : 0 (673.7 K) was lower than more structural information about the portions of the the value reported for C22 : 0 (685.0 K). For this reason, the structure where the description through the first-order value of 704.4 K reported by Yaws [153] was used. groups is insufficient. (e model constant W assumes the Figure 4 indicates the absolute relative deviation between value zero if only the first-order group estimation is taken the different methods when compared to the NIST values. into account, or one if the second order is also considered. From Figure 4, it is possible to notice that the Joback N M i and j are the group occurrences in the compound. (e and Raid method always overestimates the normal boiling coefficients used to determine the normal boiling point are point, and the overestimation increases with the molecular reported in Tables A2 and A3 of the Supplementary Material. weight. In general, for the same number of atoms of carbon Marrero-Marejon´ and Pardillo-Fontdevila proposed a in the molecule, the overestimation increases with the family of models to estimate the normal boiling point of pure unsaturation. (e same trend, but with a reduced absolute organic compounds based on the compound chemical relative deviation, is observed for the Marrero-Marejon structure and molecular weight [150]. (e normal boiling and Pardillo-Fontdevila method. (e opposite tendency is N point is evaluated according to equation (9), where i is the observed for the method developed by Constantinou and i t number of times that type occurs with contributions bbk: Gani, where the normal boiling point is underestimated for the saturated fatty acids with the highest molecular T � MW− 0.404 � N · t + 156.0. B i bbki (9) weight. A similar behaviour, but with a reduced margin of i deviations, is observed for the Marrero and Gani method. In this case, the contributions are based on group in- (e Nannoolal et al. method has a positive deviation for teraction, taking into account the interactions between the unsaturated fatty acids that seem to be independent bonding groups in the molecule. Table A4, in the Supple- from the molecular weight. However, for unsaturated fatty mentary Material, presents the coefficients used. acids, the overestimation increases with the molecular Marrero and Gani [151] defined an estimation of the weight. normal boiling point based on three levels, as follows: Table 5 shows the minimum and maximum absolute relative deviation for each method when compared with the data provided by the NIST database. T ( ) � . · ⎛⎝� N · T + � M · T + � O · T ⎞⎠. B K 222 543 ln i b1i j b2j j b3k Among all the estimation methods explored, the two- i j k level and the three-level approach proposed by Marrero and (10) Gani provided a more reliable estimation of the normal (e first level includes the simple groups used for de- boiling point for the FAs considered. scribing a wide variety of organic compounds. (e second level involves groups that permit a better description of poly- 4.1.3. Novel Normal Boiling Point Estimation Method. functional compounds and differentiation among isomers. Anand et al. [154] defined the normal boiling point for Finally, the third level provides more structural information fatty acids methyl esters (FAMEs), as a function of mo- about molecular fragments of compounds whose description is lecular weight (equation (12)). (e same approach was insufficient through the first- and second-level groups. (e followed to propose an alternative correlation for the fatty coefficients to determine the normal boiling point can be acids: found in Tables A5 and A6 of the Supplementary Material. 2 TB � A (MW) + B (MW) + C . (12) (e estimation of the boiling point proposed by FAME FAME FAME FAME Nannoolal et al. [152] is reported as follows: Using a similar equation, it was possible to obtain the coefficients to determine the normal boiling points for the �iNiCi fatty acids considered by applying the generalized reduced TB(K) � + 84.3395, (11) n0.6583 + 1.6868 gradient method to minimize the deviations. In fact, 8 International Journal of Chemical Engineering

Table 3: Methods for the normal boiling point estimation. Method Parameter(s) required Joback and Reid [148] Molecular structure Constantinou and Gani [149] Molecular structure Marrero-Marejon´ and Pardillo-Fontdevila [150] Molecular structure and MW Marrero and Gani [151] Molecular structure Nannoolal et al. [152] Molecular structure

Table 4: Comparison of experimental and estimated normal boiling temperature (K). Joback and Constantinou and Marrero-Marej´onand Marrero and Nannoolal CN : DB NIST Reid [148] Gani [149] Pardillo-Fontdevila [150] Gani [151] et al. [152] C8 : 0 512.6 528.2 512.2 518.2 517.8 516.1 C10 : 0 543.2 573.9 540.8 554.3 546.8 549.6 C12 : 0 572.1 619.7 565.9 588.3 572.5 580.0 C14 : 0 599.5 665.4 588.3 620.6 595.6 607.9 C16 : 0 619.8 711.2 608.5 651.4 616.4 633.7 C18 : 0 643.0 757.0 626.8 681.0 635.5 657.9 C20 : 0 672.9 802.7 643.7 709.5 653.1 680.6 C22 : 0 692.9 848.5 659.2 737.1 669.4 702.1 C24 : 0 704.4∗ 894.2 673.7 763.8 684.5 722.4 C16 :1 632.5 715.4 607.0 653.4 617.5 625.8 C18 :1 635.9 761.1 625.5 682.9 636.5 650.4 C20 :1 642.4 806.9 642.4 711.4 654.0 673.5 C22 :1 665.7 852.6 658.1 738.8 670.2 695.3 C24 :1 672.6 898.4 672.6 765.5 685.3 715.9 C18 : 2 624.1 765.3 624.1 684.8 637.5 643.0 C18 : 3 622.7 769.4 622.7 686.7 638.5 635.5 ∗Value reported by Yaws [153].

40 35 30 25 20 15

ARD (%) 10 5 0 –5 –10 C8:0 C10:0 C12:0 C14:0 C16:0 C18:0 C20:0 C22:0 C24:0 C16:1 C18:1 C20:1 C22:1 C24:1 C18:2 C18:3 Joback and Reid Constantinou and Gani Marrero-Marejón and Pardillo-Fontdevila Marrero and Gani Nannoolal et al.

Figure 4: Absolute relative deviation comparison for the normal boiling point estimation. observing the normal boiling point values, as a function of 2 TB � αT :n · �AA (MW) + BT (MW) FA BCN TB B :n the molecular weight, it is possible to conclude that it has a FA CN:n FA CN (13) parabolic behaviour. + C �. TB (e novel estimation method, reported in equation (13), FA CN:n A B has three coeﬃcients, assigned as TB , TB , and FA CN:n FA CN:n CT , and a correction factor, αT CN:n, which depends on (e values for AT , BT CT , and αT CN:n BFA CN:n B BFA CN:n BFA CN:n BFA CN:n B the number of unsaturation: were obtained by minimizing the relative deviations with the International Journal of Chemical Engineering 9

Table 5: Deviations of the diﬀerent methods for the normal boiling point estimation. Joback and Constantinou Marrero-Marej´onand Marrero and Nannoolal Reid [148] and Gani [149] Pardillo-Fontdevila [150] Gani [151] et al. [152] AAD (K) 119.60 11.55 43.23 10.05 15.43 RMSD (K) 133.05 16.40 49.56 12.33 18.65 AARD (%) 18.5 1.8 6.7 1.6 2.4 MIN RD (%) 3 − 5 1 − 3 − 11 MAX RD (%) 34 0 14 3 6

NIST database values, using the GRG nonlinear solving Table 6: Coefficients for the estimation of the normal boiling point method to achieve the optimized result. (e coefficients according to equation (13). obtained are presented in Table 6. (e proposed normal boiling point estimation method Coefficients Values AT − 7.0670E − 04 showed a lower estimation deviation when compared with BFA CN:n BT 0.9173 the other methods previously presented. In particular, it was BFA CN:n CT 205.6120 obtained: AAD � 8.49 K, RMSD � 11.94 K, AARD � 1.3%, BFA CN:n α 1.5697 MIN RD � − 3.6%, and MAX RD � 4.3%. TBCN:0 αTBCN:1 1.5501

αTBCN:2 1.5323 α 1.5329 4.2. Normal Melting Point. (e normal melting point for a TBCN:3 pure substance is deﬁned as the temperature in which the solid and the liquid form exist in equilibrium at atmospheric Table 7: Methods for the normal melting point estimation. pressure. In general, it is expected that the melting point of fatty acids increases if the unsaturation is reduced. If the fatty acids Method Parameter required are used for biodiesel production, the availability of the melting Joback and Reid [148] Molecular structure point is essential for the evaluation of the cold-ﬂow properties. Constantinou and Gani [149] Molecular structure Marrero and Gani [151] Molecular structure

4.2.1. Estimation Methods. Several methods are available in (e coefficients to determine the normal melting point the literature to determine the normal melting point. (e can be found in Tables A5 and A6 of the Supplementary most appropriate methods are gathered in Table 7. Material. Joback and Reid proposed the estimation formula reported as follows [148]: 4.2.2. Normal Melting Point Estimation Results. Table 8 T ( ) � . + � N · T . ( ) M K 122 5 i mi 14 presents the values of the estimated normal melting point together with the values obtained from the NIST database. According to the authors, however, estimations of the Figure 5 reports the absolute relative deviation between normal melting point are not accurate and should be considered the different methods when compared with the NIST values. only as approximate. (e coefficients of the group contributions (e Joback and Reid group contribution method are presented in Table A1 of the Supplementary Material. overestimates the normal melting point. (e overestimation (e Constantinou and Gani method [149] is presented as regularly grows for saturated fatty acids with a consistent follows: penalty for molecules with the highest molecular weight. (e same trend is observed for the unsaturated compounds even ⎛⎝ ⎞⎠ TM(K) � 102.425 × ln � Ni × Tm1i + W × � Mj × Tm2j . if the increase of the absolute relative deviation is lower with i j respect to the case of saturated fatty acids. (15) Table 9 shows the deviation indexes for each method when compared with the data provided by NIST. (e coefficients to determine the normal melting point (e method of Constantinou and Gani offers the best can be found in Tables A2 and A3 of the Supplementary estimation with a very good prediction of the saturated Material. compounds. However, for the unsaturated fatty acids, all the Marrero and Gani [151] developed a method to determine methods considered report a high estimation deviation. the normal melting point using the following equation: When comparing molecules with the same number of carbons, it is possible to observe that the melting point TM(K) � 147.450 × ln�� Ni × Tm1i + � Mj × Tm2j decreases when the unsaturation increases. (is decrease is i j due to the molecular distortion induced by the double bonds that prevent the molecules from packing together easily. (e + � Oj × Tm3k�. difficulty in predicting the London dispersion forces be- k tween the oil molecules may be the cause of the high de- (16) viations observed for unsaturated fatty acids. 10 International Journal of Chemical Engineering

Table 8: Comparison of experimental and estimated normal melting point (K). CN : DB NIST Joback and Reid [148] Constantinou and Gani [149] Marrero and Gani [151] C8 : 0 289.7 340.5 293.6 333.6 C10 : 0 304.5 363.1 303.8 341.2 C12 : 0 317.0 385.6 313.2 348.3 C14 : 0 327.3 408.1 321.7 355.1 C16 : 0 335.6 430.7 329.6 361.7 C18 : 0 342.6 453.2 336.9 367.9 C20 : 0 348.2 475.8 343.7 373.9 C22 : 0 353.8 498.3 350.1 379.7 C24 : 0 355.6 520.8 356.1 385.2 C16 :1 274.8 425.6 326.2 365.9 C18 :1 286.5 448.1 333.8 371.9 C20 :1 297.3 470.7 340.8 377.8 C22 :1 306.1 493.2 347.4 383.4 C24 :1 — 515.8 353.6 388.8 C18 : 2 267.6 443.1 330.6 375.8 C18 : 3 260.0 438.0 327.2 379.7

80 70 60 50 40 30 ARD (%) 20 10 0 –10 C8:0 C10:0 C12:0 C14:0 C16:0 C18:0 C20:0 C22:0 C24:0 C16:1 C18:1 C20:1 C22:1 C24:1 C18:2 C18:3 Joback and Reid Constantinou and Gani Marrero and Gani

Figure 5: Absolute relative deviation comparison for the normal melting point estimation.

Table 9: Deviations of different methods for the estimation of the Equation (17) is the novel estimation method developed: normal melting point. Joback and Constantinou Marrero and 2 TM � αT CN:n · �AT (MW) + BT (MW) + CT �. Reid [148] and Gani [149] Gani [151] FA M MFA MFA MFA AAD (K) 132.98 24.10 56.68 (17) RMSD (K) 141.25 34.02 65.14 AARD (%) 43.5 8.4 19.3 (e main advantage of this method is the possibility of MIN RD (%) 18 − 2 7 estimating the normal meting point, using the fatty acids’ MAX RD (%) 69 26 46 molecular weight exclusively. (e coefficients AT , BT , CT , and αT CN:n MFA CN:n MFA CN:n BFA CN:n M were obtained by minimizing the relative deviations with the 4.2.3. Novel Normal Melting Point Estimation Method. It is NIST database values. (e obtained coefficients are pre- possible to obtain the coefficients to determine the normal sented in Table 10. melting points applying the generalizedreduced gradient For the proposed method, the comparison indexes are (GRG) method to minimize the deviations, with a similar AAD � 3.15 K, RMSD � 4.09 K, AARD � 1.0%, MIN RD � procedure described in Section 4.1.3 for the estimation of the − 2.6%, and MAX RD � 3.1%, giving a smaller deviation normal boiling point. when compared to the other estimation methods. International Journal of Chemical Engineering 11

4.3. Critical Parameters. (e critical point is used to Table 10: Coefficients for the estimation of the normal melting identify the fluid region where the liquid and gas phases point according to equation (17). can be no longer distinguished. Critical parameters are Coefficients Values used for the estimation of other properties, such as the AT − 4.1905E − 04 acentric factor, compressibility factor, liquid density, MFA CN:n BT 0.4863 vapor pressure, and enthalpy of vaporization, among MFA CN:n CT 193.9418 others. MFA CN:n αTMCN:0 1.1380

αTMCN:1 0.9752 α 0.8999 4.3.1. Estimation Methods. Several methods are available in TMCN:2 α 0.8759 the literature to determine the critical parameters such as TMCN:3 critical temperature, critical pressure, and critical volume. (e most appropriate methods are summarized in ⎛⎝ ⎞⎠ TC (K) � 181.128 · ln � Ni · Tc1i + W · � Mj · Tc2j , Table 11. i j Joback and Reid proposed the relations reported in (21) equations (18)–(20) to estimate the critical properties based on the group contribution methods [148]: − 2

PC (bar) � �� Ni · Pc1i + W × � Mj · Pc2j + 0.100220� T i j T � B , C 2 (18) . + . � N · T − �� N · T � + 1.3705, 0 584 0 965 i ci i ci (22) 1 P � , C 2 (19) �0.113 + 0.0032NA − � Ni · Pc � 3 − 1 ⎛⎝ ⎞⎠ i VC �cm ·mol � � − 0.004350 + � Ni · vc1i + W × � Mj · vc2j . i j V � . + � N · V , ( ) C 17 5 i ci 20 (23) where NA is the number of atoms in the molecule. (e (e coeﬃcients to determine the critical properties can be T P V found in Tables A2 and A3 in the Supplementary Material. values ci, ci, and ci are presented in Table A1. Constantinou and Gani [149] established a method to Wilson and Jasperson suggested equation (24) to esti- determine TC, PC, and VC using equations (21)–(23), mate the critical temperature and equation (25) to determine respectively: the critical pressure:

T T ( ) � B , C K 0.2 (24) �0.048271 − 0.019846Nr + �kNk · tck + �jMjΔtcj�

0.0186233 · TC PC (bar) � . (25) − 0.96601 + exp �− 0.0092295 − 0.0290403Nr + 0.041��kNk · Pcbk + �jMjΔPcj��

(e coeﬃcients to determine these critical properties can and vcbk. (e parameters to determine these critical parameters be found in Table A6 in the Supplementary Material. can be found at Table A4 in the Supplementary Material. Marrero-Marejo´n and Pardillo-Fontdevila developed Marrero and Gani [151] determined TC, PC, and VC equations (26)–(28) to calculate the critical parameters [150]: using the following equations:

TB TC (K) � 2, . − . � N · t � +�� M · t � 0 5851 0 9286 k k bck j j Δ cbj TC (K) � 231.239· ln��Ni ·Tc1i +W·�Mj ·Tc2j (26) i j (29) − 2 +W·�Ok ·Tc3k�, ⎛⎝ ⎞⎠ k PC (bar) � 0.1285 − 0.0059Natoms − �Nk · Pcbk , k (27) ⎛⎝ PC (bar) � �Ni ·Pc1i +W×�Mj ·Pc2j +W 3 − 1 VC �cm · mol � � − 25.1 + �Nk · vcbk, (28) i j k − 2 (30) ⎞⎠ where Natoms is the number of atoms in the compound and Nk ×�Ok ·Pc3k +0.108998 +5.9827, is the number of atoms of type k with contributions tcbk, pcbk, k 12 International Journal of Chemical Engineering

Table 11: Methods for the critical parameters’ estimation. Method Parameter(s) required

Joback and Reid [148] Molecular structure and TB Constantinou and Gani [149] Molecular structure Wilson and Jasperson [155] Molecular structure and TB Marrero-Marejon´ and Pardillo-Fontdevila [150] Molecular structure and TB Marrero and Gani [151] Molecular structure Nannoolal et al. [156] Molecular structure, MW, and TB

give the best results. When one or more unsaturations are 3 − 1 ⎛⎝ VC �cm ·mol � � 7.95+ �Ni ·Vc1i +W×�Mj ·Vc2j considered, it is not possible to define a method that i j consistently predicts the critical temperature. Table 13 shows the minimum and maximum absolute relative de- ⎞⎠ viation for each method when compared with the data + W×�Ok ·Vc3k . k provided by NIST. (31) From the analysis of Table 13, it is possible to notice that the Constantinou and Gani’s method exhibits the (e coefficients to determine the critical properties can best global performances for the critical temperature be found in Tables A5 and A6 in the Supplementary estimation. Material. (e estimation of the critical properties proposed by (2) Critical Pressure Estimation Results. (e results for the Nannoolal et al. [156] is presented in the following estimated critical pressures and the experimental values for equations: the fatty acids are presented in Table 14. Figure 7 presents the relative deviation between the ⎛⎝ 1 ⎞⎠ estimated values and the ones gathered from the NIST TC (K) � TB 0.6990 + 0.8607 , 0.9889 +�iNiCi � database. All the methods provide estimations included in (32) a range of deviation of ±10%, except for the Marrero and Gani method when applied to saturated fatty acids with MW− 0.14041(g/mol) high molecular weight and unsaturated fatty acids with PC (kPa) � 2, (33) one and three double bonds. (e Nannoolal et al. method 0.00939 + �iNiCi� gives the best estimation for the fatty acids at high molecular weight with one double bond. Regarding the � N C V �cm3 · mol− 1 � � i i i + 86.1539, (34) saturated compounds, the Marrero-Marejoń and Pardillo- C n− 0.2266 Fontdevila method overestimates the critical pressure until C16 : 0. After this component, there is an un- where n is the number of atoms in the molecule (excluding derestimation that increases linearly with the molecular hydrogen). Table A7 in the Supplementary Material presents weight. Apart from the Marrero and Gani method, all the the coefficients used. others underestimate the critical pressure in the range of For the estimation methods that depend on the normal C16 : 0–C22 : 0. boiling point temperature, this value can be experimentally Table 15 shows the minimum and maximum absolute determined or estimated. (e calculations were performed relative deviation for each method when compared with the using the normal boiling point temperatures available from data provided by NIST. the NIST database, as reported in Table 4. (3) Critical Volume Estimation Results. (e estimated and 4.3.2. Critical Properties Estimation Results experimental values for the fatty acids’ critical volume are presented in Table 16. (1) Critical Temperature Estimation Results. (e estimated Figure 8 presents the relative deviation distribution and experimental values for the critical temperatures are between the estimated values and the ones provided by presented in Table 12. NIST. Figure 6 presents the absolute relative deviation between (e Nannoolal et al. method offers the best prediction the methods considered and the NIST database values. for the saturated compounds with a peak of about 10% Except for the Marrero and Gani’s method, all the other overestimation for C24 : 0. However, the overestimation methods have a general agreement until the C16 : 0. For the increases to 20% when the unsaturated compounds are compounds with higher molecular weight, the method evaluated. All the other methods exhibit an opposite be- developed by Nannoolal et al. and by Constantinou and Gani haviour, with the tendency to underestimate the critical International Journal of Chemical Engineering 13

Table 12: Comparison of experimental and estimated critical temperature (K). Joback and Wilson and Constantinou Marrero-Marej´onand Marrero and Nannoolal CN : DB NIST Reid [148] Jasperson [155] and Gani [149] Pardillo-Fontdevila [150] Gani [151] et al. [156] C8 : 0 693.7 692.1 694.6 695.0 692.3 738.2 694.9 C10 : 0 723.8 714.6 718.4 720.4 715.7 762.3 719.5 C12 : 0 743.0 736.6 740.5 742.7 739.1 784.0 742.0 C14 : 0 763.0 758.4 760.8 762.5 762.8 803.9 762.5 C16 : 0 785.0 773.5 772.7 780.4 780.4 822.2 774.3 C18 : 0 803.0 794.5 788.7 796.6 804.6 839.2 790.1 C20 : 0 820.0 826.2 813.0 811.6 840.4 855.0 814.1 C22 : 0 837.0 848.4 825.5 825.4 867.4 869.8 826.3 C24 : 0 825.0 863.1 828.2 838.2 887.6 883.7 828.6 C16 :1 789.0 792.5 791.3 780.0 800.7 825.1 796.3 C18 :1 775.0 787.9 782.4 796.3 798.1 841.8 786.9 C20 :1 811.0 790.1 778.4 811.3 802.8 857.5 782.4 C22 :1 806.0 815.6 795.3 825.1 831.9 872.1 798.8 C24 :1 838.0 823.7 792.9 837.9 844.0 885.9 795.8 C18 : 2 787.0 775.8 770.4 796.0 786.6 844.5 778.0 C18 : 3 777.0 776.8 771.2 795.7 789.3 847.1 782.1

10 8 6 4 2 0 ARD (%) –2 –4 –6 –8 C8:0 C10:0 C12:0 C14:0 C16:0 C18:0 C20:0 C22:0 C24:0 C16:1 C18:1 C20:1 C22:1 C24:1 C18:2 C18:3 Joback and Reid Wilson and Jasperson Constantinou and Gani Marrero-Marejón and Pardillo-Fontdevila Marrero and Gani Nannoolal et al.

Figure 6: Absolute relative deviation of estimation for the critical temperature.

Table 13: Deviations of diﬀerent methods for the estimation of the critical temperature. Joback and Wilson and Constantinou Marrero-Marejon´ and Marrero and Nannoolal Reid [148] Jasperson [155] and Gani [149] Pardillo-Fontdevila [150] Gani [151] et al. [156] AAD (K) 10.64 11.23 7.95 13.80 47.23 10.14 RMSD (K) 13.72 16.13 10.57 20.85 48.77 14.62 AARD (%) 1.3 1.4 1.0 1.7 6.0 1.3 MIN RD (%) − 3 − 5 − 1 − 1 4 − 5 MAX RD (%) 2 1 3 4 9 2 volume for saturated compounds, with a lower deviation for 4.3.3. Novel Critical Parameters Estimation Method the unsaturated fatty acids. Table 17 shows the minimum and maximum absolute (1) Novel Critical Temperature Estimation Method. Anand relative deviation for each method when compared with the et al. [154] proposed a critical temperature estimation data provided by the NIST database. method for FAMEs, according to the following: Except for the Nannoolal et al. method, that is only recommended for saturated compounds, all the other methods 2 TC � AT (MW) + BT (MW) + CT . (35) provide a general agreement in the critical volume estimation. FAME CFAME CFAME CFAME 14 International Journal of Chemical Engineering

Table 14: Comparison of experimental and estimated critical pressure (bar). Joback and Wilson and Constantinou and Marrero-Marej´onand Marrero and Nannoolal CN : DB NIST Reid [148] Jasperson [155] Gani [149] Pardillo-Fontdevila [150] Gani [151] et al. [156] C8 : 0 28.57 27.79 26.91 27.67 31.07 26.87 26.27 C10 : 0 20.76 22.92 22.22 22.79 25.40 22.52 22.11 C12 : 0 19.31 19.22 18.79 19.14 21.16 19.40 18.87 C14 : 0 16.40 16.35 16.17 16.36 17.89 17.09 16.29 C16 : 0 14.90 14.08 13.96 14.18 15.33 15.33 14.21 C18 : 0 13.30 12.25 12.25 12.44 13.28 13.95 12.50 C20 : 0 12.00 10.76 10.97 11.03 11.62 12.86 11.07 C22 : 0 11.10 9.52 9.75 9.88 10.25 11.98 9.88 C24 : 0 8.49 8.49 8.61 8.92 9.11 11.25 8.86 C16 :1 14.88 14.65 14.58 14.15 15.86 15.52 14.37 C18 :1 13.90∗ 12.71 12.39 12.42 13.71 14.10 12.63 C20 :1 10.98 11.13 10.69 11.02 11.96 12.98 11.18 C22 :1 9.83 9.83 9.55 9.87 10.53 12.07 9.97 C24 :1 8.87 8.75 8.61 8.91 9.35 11.33 8.94 C18 : 2 14.10 13.19 12.43 12.40 14.15 14.25 12.76 C18 : 3 12.34∗ 13.71 12.68 12.38 14.62 14.41 12.89 ∗Values retrieved from the database APV88 PURE32 of Aspen Plus.

10 ARD (%) 0

–10

–20 C8:0 C10:0 C12:0 C14:0 C16:0 C18:0 C20:0 C22:0 C24:0 C16:1 C18:1 C20:1 C22:1 C24:1 C18:2 C18:3 Joback and Reid Wilson and Jasperson Constantinou and Gani Marrero-Marejón and Pardillo-Fontdevila Marrero and Gani Nannoolal et al.

Figure 7: Absolute relative deviation of estimation for the critical pressure.

Table 15: Deviations of diﬀerent methods for the estimation of the critical pressure. Joback and Wilson Constantinou Marrero-Marejon´ Marrero and Nannoolal NIST Reid [148] and Jasperson [155] and Gani [149] and Pardillo-Fontdevila [150] Gani [151] et al. [156] AAD (bar) 0.73 0.83 0.71 1.15 1.23 0.77 RMSD (bar) 0.98 0.99 0.95 1.64 1.50 0.97 AARD (%) 5.1 5.7 4.9 7.5 10.4 5.1 MIN RD (%) − 14 − 12 − 12 − 8 − 6 − 11 MAX RD (%) 11 7 10 22 33 7 Globally, the Nannoolal et al. method oﬀers a better estimation together with the Constantinou and Gani approach.

Using a similar equation, it is possible to obtain the 2 TC (K) � αT CN:n · �AT (MW) + BT (MW) + CT �. coeﬃcients to determine the critical temperature for the fatty FA C CFA CFA CFA acids applying the generalized reduced gradients method to (36) minimize the deviations. Equation (36) is the novel esti- (e coeﬃcients AT , BT , CT , and αT CN:n mation method proposed to estimate the fatty acids critical CFA CN:n CFA CN:n CFA CN:n C temperature: were obtained by minimizing the relative deviations with the International Journal of Chemical Engineering 15

Table 16: Comparison of experimental and estimated critical volume (m3/kmol). Joback and Constantinou and Marrero-Marejon´ and Marrero Nannoolal CN : DB NIST Reid [148] Gani [149] Pardillo-Fontdevila [150] and Gani [151] et al. [156] C8 : 0 0.526 0.5075 0.5071 0.5107 0.5046 0.5267 C10 : 0 0.639 0.6195 0.6187 0.6239 0.6172 0.6579 C12 : 0 0.787 0.7315 0.7302 0.7371 0.7298 0.7948 C14 : 0 0.921 0.8435 0.8417 0.8503 0.8423 0.9367 C16 : 0 1.066 0.9555 0.9532 0.9635 0.9549 1.0831 C18 : 0 1.255 1.0675 1.0647 1.0767 1.0674 1.2335 C20 : 0 1.371 1.1795 1.1763 1.1899 1.1800 1.3877 C22 : 0 1.486 1.2915 1.2878 1.3031 1.2926 1.5453 C24 : 0 1.575 1.4035 1.3993 1.4163 1.4051 1.7062 C16 :1 0.898 0.9355 0.9399 0.9429 0.9409 1.0525 C18 :1 1.016 1.0475 1.0514 1.0561 1.0535 1.2022 C20 :1 1.158 1.1595 1.1630 1.1693 1.1660 1.3557 C22 :1 1.448 1.2715 1.2745 1.2825 1.2786 1.5127 C24 :1 1.402 1.3835 1.3860 1.3957 1.3911 1.6729 C18 : 2 0.972 1.0275 1.0381 1.0355 1.0395 1.1708 C18 : 3 0.960 1.0075 1.0248 1.0149 1.0255 1.1395

25 20 15 10 5 0 ARD (%) –5 –10 –15 –20 C8:0 C10:0 C12:0 C14:0 C16:0 C18:0 C20:0 C22:0 C24:0 C16:1 C18:1 C20:1 C22:1 C24:1 C18:2 C18:3 Joback and Reid Constantinou and Gani Marrero-Marejón and Pardillo-Fontdevila Marrero and Gani Nannoolal et al.

Figure 8: Absolute relative deviations of estimation for the critical volume.

NIST database values. (e coefficients obtained are pre- NIST database values, using the GRG nonlinear solving sented in Table 18. method to find the optimized result. (e obtained co- For the proposed method, the critical temperature de- efficients are presented in Table 19. viations resulted in AAD � 5.88 K, RMSD � 8.01 K, For the proposed method, the critical pressure deviations AARD � 0.7%, MIN RD � − 1.6%, and MAX RD � 2.3% resulted in AAD � 0.69 bar, RMSD � 0.94 bar, AARD � 4.6%, compared with NISTdatabase. (us, AAD, RMSD, and AARD MIN RD � − 10.4%, and MAX RD � 9.7%. Again, AAD, significantly outperform the estimation methods considered. RMSD, and AARD show an improvement in accuracy, when compared with the considered estimation methods. (2) Novel Critical Pressure Evaluation Method. Applying the same procedure, it is possible to optimize equation (37) in (3) Novel Critical Volume Estimation Method. Applying the order to obtain a functional equation to estimate the critical same procedure as it was suggested before, it is possible to pressure: derive equation (38) to estimate the critical volume:

2 2 PC (bar) � αP :n · �AP (MW) + BP (MW) + CP �. VC (mL/mol) � αV CN:n · �AV (MW) FA CCN C C C FA C CFA FA FA FA (38) (37) + BV (MW) + CV �. CFA CFA

(e coeﬃcients AP , BP , CP , and αP CN:n (e coeﬃcients AV , BV , CV , and αV CN:n CFA CN:n CFA CN:n CFA CN:n C CFA CN:n CFA CN:n FA CN:n C were obtained by minimizing the relative deviations with the were obtained by minimizing the relative deviations with the 16 International Journal of Chemical Engineering

Table 17: Deviations of diﬀerent methods for the estimation of the critical volume. Joback and Constantinou and Marrero-Marej´onand Marrero and Nannoolal Reid [148] Gani [149] Pardillo-Fontdevila [150] Gani [151] et al. [156] AAD (m3/kmol) 0.087 0.091 0.084 0.090 0.096 RMSD (m3/kmol) 0.112 0.114 0.106 0.112 0.130 AARD (%) 7.3 7.6 7.0 7.6 8.6 MIN RD (%) − 5 − 15 − 15 − 14 − 15 MAX RD (%) 31 6 7 7 7

Table 18: Coefficients for the estimation of the critical temperature Table 19: Coefficients for the estimation of the critical pressure according to equation (36). according to equation (37). Coefficients Values Coefficients Values

AT − 1.8345E − 03 AP 7.0357E − 04 CFA CN:n CFA CN:n BT 1.6239 BP − 0.5776 CFA CN:n CFA CN:n CT 550.5882 CP 143.4049 CFA CN:n CFA CN:n αTCCN:0 0.9286 αPCCN:0 0.3515

αTCCN:1 0.9185 αPCCN:1 0.3556

αTCCN:2 0.9134 αPCCN:2 0.3836

αTCCN:3 0.9028 αPCCN:3 0.3323

NIST database values, using the GRG nonlinear solving Table 20: Coefficients for the estimation of the critical volume method to achieve the optimized result. (e obtained co- according to equation (38). efficients are presented in Table 20. (e proposed method for the critical volume yield de- Coefficients Values 3 3 � . ( ) � . ( ) AV − 1.0023E − 06 viations of AAD 0 03 m /kmol , RMSD 0 05 m / kmol , CFA CN:n BV 0.0206 AARD � 2.1%, MIN RD � − 13.6%, and MAX RD � 3.1%. CFA CN:n CV − 0.9068 (e first three indicators significantly outperform the ones CFA CN:n α 0.2485 computed for the considered estimation methods. VCCN:0 αVCCN:1 0.2106

αVCCN:2 0.2033

4.4. Acentric Factor. (e acentric factor (ω) is a pure αVCCN:3 0.2025 component constant that indicates the acentricity or nonsphericity of a molecule. Monoatomic molecules are Table 21: Methods for the estimation of the acentric factor. expected to have acentric factors equal to zero, and their values increase with the molecular weight and polarity Method Parameters required [155]. Pitzer et al. [158] Vapor pressure and PC (is property is used in the estimation of transport and Lee and Kesler [159] TB,TC,PC thermodynamic properties for gases and liquids, such as Watanasiri et al. [160] Speciﬁc gravity, MW,TB compressibility factor, heat capacity, enthalpy of vapor- Ambrose and Walton [161] TB,TC,PC ization, and saturated density [155, 157]. Chen et al. [157] TB,TC,PC Constantinou et al. [162] Molecular structure

4.4.1. Estimation Method. Several methods are available in P the literature to determine the acentric factor. (e most where r is the reduced vapor pressure, deﬁned as P � Pvap P Pvap appropriate methods are summarized in Table 21. r / C , and is the vapor pressure at temperature T T T � . (e acentric factor was initially proposed by Pitzer et al., , deﬁned at the reduced temperature / C 0 7. (e and it is given by the following equation [158]: vapor pressure can be determined by the NIST Wagner Equation, given as follows: ω � − log10 Pr − 1.0, (39)

× − T C �� + × − T C ��1.5 + × − T C ��2.5 + × − T C ��5 vap C1 1 / 6 C2 1 / 6 C3 1 / 6 C4 1 / 6 ( ) lnP � � C5 + , 40 T/C6 International Journal of Chemical Engineering 17

6 where the pressure is given in Pa. (e coeﬃcients C1, C2, C3, − ln PC − 5.92714 + 6.09648/TBr� + 1.28862 ln TBr + 0.169347 TBr ω � 6 , C4, C5, and C6 can be found in Table A7 of the Supple- 15.2518 − 15.6875/TBr� − 13.4721 ln TBr + 0.43577 TBr mentary Material. (41) (e parameter proposed by Pitzer et al. is, however, limited to reduced temperatures above 0.8. where TBr � TB/TC is the reduced temperature at the boiling Lee and Kesler proposed an analytical correlation for the point. acentric factor employing equations of state, based on a wide Watanasiri et al. developed a correlation to estimate the variety of compounds. (eir goal was to improve the rep- acentric factor based on heterocyclic compounds and other resentation of the property at low temperatures and near the hydrocarbons and their derivatives [160]. According to critical region [159]. (e proposed equation (41) is given as their model, the acentric factor is given by the following follows: equation:

T 382.904 T 2 ω � ⎡⎣0.92217 × 10− 3 T + 0.507288 B + + 0.242 × 10− 5�B � − 0.2165 × 10− 4 T × MW + 0.1261 × 10− 2 SG B MW MW SG B

T1/3 T2/3 T × MW + 0.1265 × 10− 4 MW2 + 0.2016 × 10− 4 SG × MW2 − 80.6495 B − 0.3738 × 10− 2 B ⎤⎦�B �, MW SG2 MW (42) where SG is the specific gravity of the component. Values of lnP /1.01325 � + f(0) ω � − C , (43) specific gravity were obtained from the NIST database. f(1) According to Poling et al. [155], the most accurate ( ) technique to obtain an unknown acentric factor is from the where the critical pressure is in bar and the functions f 0 (1) critical temperature and pressure combined with the normal and f are defined as functions of TBr. (ese functions are boiling point. (ey have found that the most reliable method obtained according to the equations proposed by Ambrose is given as follows: and Walton [161]:

. . − 5.97616 1 − T � + 1.29874 1 − T �1 5 − 0.60394 1 − T �2 5 − 1.06841 1 − T �5 f(0) � Br Br Br Br , (44) TBr

. . − 5.03365 1 − T � + 1.11505 1 − T �1 5 − 5.41217 1 − T �2 5 − 7.46628 1 − T �5 f(1) � Br Br Br Br . (45) TBr

(e method proposed by Chen et al. requires the same where ω1i is the contribution of the ﬁrst-order group type i properties for the estimation of the acentric factor. However, occurring Ni times and ω2j is the contribution of the second- this work suggested a correlation based on the Antoine order group type j occurring Mj times. (e coeﬃcients to Equation [157]. Based on 217 compounds over the broadest determine the acentric factor can be found in Tables A2 and possible range of TBr, the acentric factor can be estimated as A3 of the Supplementary Material. follows:

0.3 0.2803 + 0.4789 T �log P 4.4.2. Acentric Factor Estimation Results. Estimated values ω � Br C − 1. (46) of the acentric factor are given in Table 22. 1 − T � 0.9803 − 0.5211 T � Br Br Figure 9 presents the relative deviation between the diﬀerent methods when compared to the NIST values, while Furthermore, Constantinou et al. proposed a method for Table 23 shows the minimum and maximum absolute rel- the estimation of the acentric factor using group contri- ative deviation for each method when compared with the bution [162]. (e equation for the property estimation is data provided by NIST. reported as follows: (e acentric factor provided by NIST is obtained from the Pitzer correlation. (e relative deviation concerning the ω 0.5050 components C20 :1 and C24 :1 is higher for the methods exp � � � � N ω + � M ω + 1.1507, 0.4085 i 1i j 2j proposed by Watanasiri et al. and Constantinou et al. (is i i occurs since the estimation of the vapor pressure was not (47) available in the NISTdatabase. (erefore, the NIST values of 18 International Journal of Chemical Engineering

Table 22: Comparison of experimental and estimated acentric factor. Pitzer et al. Lee and Kesler Watanasiri Ambrose and Walton Chen et al. Constantinou et al. CN : DB NIST [158] [159] [160] [161] [157] [162] C8 : 0 0.782 0.782 0.790 0.493 0.776 0.776 0.780 C10 : 0 0.749 0.749 0.725 0.495 0.709 0.712 0.861 C12 : 0 0.879 0.879 0.889 0.532 0.869 0.872 0.940 C14 : 0 0.940 0.940 0.965 0.605 0.940 0.946 1.017 C16 : 0 0.970 0.970 0.942 0.714 0.917 0.925 1.093 C18 : 0 1.029 1.029 1.001 0.863 0.973 0.984 1.167 C20 : 0 1.184 1.184 1.206 1.031 1.171 1.187 1.239 C22 : 0 1.233 1.233 1.252 1.243 1.215 1.234 1.310 C24 : 0 0.810 0.810 1.449 1.508 1.403 1.437 1.379 C16 :1 1.088 1.088 1.105 0.751 1.075 1.084 1.079 C18 :1 1.247 1.345 1.342 0.856 1.304 1.315 1.153 C20 :1 0.725 — 0.742 1.184 0.719 0.736 1.226 C22 :1 1.080 1.080 1.102 1.294 1.068 1.091 1.297 C24 :1 0.676 — 0.694 1.766 0.671 0.694 1.366 C18 : 2 0.996 0.956 0.945 1.043 0.920 0.929 1.140 C18 : 3 1.022 0.976 0.950 1.054 0.922 0.936 1.127

200

150

100

ARD (%) 50

–50 C8:0 C10:0 C12:0 C14:0 C16:0 C18:0 C20:0 C22:0 C24:0 C16:1 C18:1 C20:1 C22:1 C24:1 C18:2 C18:3 Ambrose and Walton Watanasiri Constantinou and Gani Lee amd Kesler Pitzer Chen

Figure 9: Absolute relative deviation of estimation of the acentric factor. the acentric factor for these two components were probably (e acentric factor has a deﬁnition based on vapor estimated using another method. In addition, the acentric pressure. In this way, the property is indirectly measured, factor of the component C24 : 0 is inconsistent when which can result in uncertainties in the estimation. (e compared to the other saturated fatty acids, which makes estimation of the acentric factor for the unsaturated fatty this value doubtful. Once the Pitzer equation was used for acids as well as the component C24 : 0 reported some the estimation of the values from NIST, the absolute de- inconsistencies. Disregarding those fatty acids, the av- viation of Pitzer regarding the NIST acentric value is erage absolute relative deviation of the methods reduced negligible. to 0% for Pitzer et al., 2.1% to Lee and Kesler method, (e method proposed by Watanasiri et al. reported a 25.3% for Watanasiri, 2.6% for Ambrose and Walton, higher deviation with respect to NIST. (is is due to the fact 2.1% for Chen et al., and 8.4% for the method proposed that, in their study, the correlations were built using a by Constantinou et al. (erefore, these estimations are diﬀerent set of components that did not include fatty acids. more reliable for the saturated fatty acids from C8 : 0 to Followed by this method, Constantinou et al. reported the C22 : 0. second-highest deviation since their estimation was made by using the group contributions instead of the physical properties of the components. Conversely, the methods by 4.4.3. Novel Acentric Factor Estimation Method. (e novel Lee and Kesler, Ambrose and Walton, and Chen et al. have method proposed to estimate the acentric factor is given as reported low deviation compared to NIST. follows: International Journal of Chemical Engineering 19

Table 23: Deviations of diﬀerent methods for the prediction of the acentric factor. Pitzer et al. Lee and Kesler Watanasiri Ambrose and Walton Chen et al. Constantinou et al. [158] [159] [160] [161] [157] [162] AAD (K) 0.01 0.07 0.32 0.07 0.07 0.19 RMSD (K) 0.03 0.16 0.41 0.15 0.16 0.27 AARD (%) 1.2 7.8 37.7 7.5 7.5 22.6 MIN RD (%) − 4 − 7 − 40 − 10 − 8 − 7 MAX RD (%) 8 79 161 73 77 102

Table 24: Coeﬃcients for the estimation of the acentric factor (valid from C8 : 0 to C22 : 0) according to equation (48). Coeﬃcients Values A 5.4382E − 05 ωFA CN:n B − 0.0032 ωFA CN:n C 6.4600 ωFA CN:n αωCN:0 0.1066

Table 25: Coeﬃcients for the estimation the temperature nondependent properties according to equation (49).

Coeﬃcients TB TM TC PC VC ω A − 7.0670E − 04 − 4.1905E − 04 − 1.8345E − 03 7.0357E − 04 − 1.0023E − 06 5.4382E − 05 B 0.9173 0.4863 1.6239 − 0.5776 0.0206 − 0.0032 C 205.6120 193.9418 550.5882 143.4049 − 0.9068 6.4600 αCN:0 1.5697 1.1380 0.9286 0.3515 0.2485 0.1066 αCN:1 1.5501 0.9752 0.9185 0.3556 0.2106 — αCN:2 1.5323 0.8999 0.9134 0.3836 0.2033 — αCN:3 1.5329 0.8759 0.9028 0.3323 0.2025 —

2 Different unsaturated fatty acids with 1, 2, or 3 double ω � αω CN:n ×�Aω FA(MW) + Bω FA(MW) + Cω FA�. bonds were considered. (48) Among the saturated fatty acids, the highest average yields were found for palmitic (C16 : 0) and stearic (C18 : 0) (e coefficients AP , BP , CP , and αP CN:n CFA CN:n CFA CN:n CFA CN:n M acids, with a value of around 15 and 5%, respectively. (e were obtained by minimizing the relative deviations between highest yields for the unsaturated fatty acids were found for the values estimated by the novel method and the NIST oleic (C18 :1), linoleic (C18 : 2), and linolenic (C18 : 3) acids, database values, using the GRG nonlinear solving method to at around 32, 27, and 7%, respectively. (e frequency of achieve the optimized result. palmitic (C16 : 0), stearic (C18 : 0), oleic (C18 :1), and As the variability of the NIST database is very high, linoleic (C18 : 2) acids is around 100% since almost all the mainly for the unsaturated fatty acids, the novel method will selected biomasses have these four fatty acids. be only valid to estimate the acentric factors for fatty acids Available estimation methods for the temperature within the range between C8 : 0 and C22 : 0. (e coefficients nondependent properties, such as normal boiling point, to determine the acentric factor are provided in Table 24. normal melting point, critical properties, and acentric factor, For the novel method for the acentric factor, were compared, and novel estimation methods were de- � . � . � . � AAD 0 03 K, RMSD 0 03 K, AARD 3 0%, MIN RD veloped to enhance their predictions. (e novel proposed − . � . 3 0%, and MAX RD 7 1%. method is simple to use, and it is based on the molecular weight and the maximum number of double bonds in the 5. Conclusions molecule. (is method is generalized in equation (49), where PP is the temperature nondependent physical property: Over one hundred biomass sources were reviewed, and 16 2 saturated, unsaturated, and polyunsaturated fatty acids PP � αCN:n · �A(MW) + B(MW) + C�. (49) were selected, based on their frequency and amount. (e selected saturated fatty acids ranged from C8 to C24, in (e three coefficients, assigned as A, B, and C, and the agreement with Kenar et al. [163], which states that “sat- correction factor αTBCN:n, which depends on the number of urated fatty acids having alkyl chain lengths greater than 18 unsaturation, are summarized in Table 25. carbon atoms are often negligible in most seed oils and are For all the properties, new equations provide a better only found at useful levels in a few unusual seed oils.” estimation with an absolute average deviation equal to or 20 International Journal of Chemical Engineering lower than 4.6%, compared to the values of the NIST da- fluid extraction of oil from industrial grape seeds,” ?e Journal tabase used as reference. (is approach allows a better fatty of Supercritical Fluids, vol. 141, pp. 68–77, 2018. acid property prediction compared to other previously [5] J. Kannengiesser, K. Sakaguchi-Soder,¨ T. Mrukwia, J. Jager, published methods. and L. Schebek, “Extraction of medium chain fatty acids It should be highlighted that the classic group contri- from organic municipal waste and subsequent production of bution methods have been developed to be applied to a wide bio-based fuels,” Waste Management, vol. 47, pp. 78–83, range of chemical compounds and different research groups 2016. [6] A. B. Fadhil, L. A. Saleh, and D. H. Altamer, “Production of implemented various corrections to take into account the biodiesel from non-edible oil, wild mustard (Brassica Juncea L.) possible interaction between different molecule fragments. seed oil through cleaner routes,” Energy Sources, Part A: Re- However, the validity of the equations developed in this covery, Utilization, and Environmental Effects, pp. 1–13, 2019. work is limited for the fatty acids selected. [7] N. M. T. Al-layla, D. H. Altamer, and S. H. Sedeeq, “Biodiesel (e equations proposed represent an improvement in production from wild mustard (Brassica Juncea L.) seed oil the modelling of processes related to the recovery and through co-solvent method at room temperature,” In- purification of fatty acids from biomasses. Indeed, these ternational Journal of Innovative Technology and Exploring equations have the potential to become a stepping stone Engineering, vol. 8, no. 4S2, pp. 83–87, 2019. for investigations of fatty acid mixtures or triglycerides [8] A. K. Agarwal, “Biofuels (alcohols and biodiesel) applications [4], taking into account that the first step in process as fuels for internal combustion engines,” Progress in Energy modelling relies on accurately predicting their physical and Combustion Science, vol. 33, no. 3, pp. 233–271, 2007. properties. [9] M. R. Patel, P. S. Chitte, and D. P. Bharambe, “Oleic acid based polymeric flow improvers for Langhnaj (North Data Availability Gujarat, India) crude oil,” Egyptian Journal of Petroleum, vol. 26, no. 4, pp. 895–903, 2017. (e data used to support the findings of this study are in- [10] O. P. Akinyemi, J. D. Udonne, V. E. Efeovbokhan, and cluded within the supplementary information file. A. A. Ayoola, “A study on the use of plant seed oils, trie- thanolamine and xylene as flow improvers of Nigerian waxy crude oil,” Journal of Applied Research and Technology, Conflicts of Interest vol. 14, no. 3, pp. 195–205, 2016. (e authors declare that there are no conflicts of interest. [11] J. Zhang, Z. Guo, W. Du et al., “Preparation and performance of vegetable oils fatty acids hydroxylmethyl triamides as crude oil flow improvers,” Petroleum Chemistry, vol. 58, Acknowledgments no. 12, pp. 1070–1075, 2018. (e financial support from Fundação para a Cienciaˆ e a [12] Z. Hungerford, K. D. Beare, A. K. L. Yuen, A. F. Masters, and T. 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